Modeling of Power/Ground Planes Using Triangular Elements

Abstract

As the operating frequency of electronic devices increases and system miniaturization continues, designing power delivery networks (PDNs) that supply quality power throughout the system becomes very challenging. To guarantee successful performance of the PDN, an accurate and time-efficient simulation method that computes the PDN impedance is required. In this paper, we propose a computationally efficient PDN modeling method that analyzes multilayer power/ground planes. The proposed method solves the differential form of Maxwell's equation applied on the circuit representation of a plane pair. To use the analogy between the equations of the electromagnetic field and the equivalent circuit, a dual mesh is created on the metal surface. The use of a nonuniform triangular mesh enables effective discretization of multidimensional and irregular geometries. Moreover, the differential equation generates a sparse system matrix, which requires small computer resources. The proposed model is extended to multiple plane pairs, and the modeling of apertures located on any layer is also included. Simulation results show that the proposed method can solve complex structures with less computational effort than other modeling methods, while maintaining accuracy. In addition, the application of the absorbing boundary condition (ABC) to the proposed method is presented. Applying ABC to the plane boundaries prevents outgoing waves from reflecting back into the plane pair, hence removing plane resonances. The use of the first-order ABC results in a simple implementation and the results show good correlation with the results from a full-wave solver using higher order ABC.